Quadratic equations

1. When solving a quadratic equation using the quadratic formula, it is possible for the b2 - 4ac term inside the square root (the discriminant) to be negative, thus forcing us to take the square root of a negative number. The solutions to the equation will then be complex numbers (i.e., involve the imaginary unit i). Question: In the real world, where might these so-called imaginary numbers be used? 2. When using a formula, we often know the value of one variable to a greater degree of accuracy than we know the others. In your opinion, what affect, if any, does it make on our use of a formula if we know the value of one variable to a greater degree of accuracy than another?

Orthogonal matrix

Show that if Q satisfies = for all x and y in R^n, then Q is orthogonal. Could you help to explain in detail? Thx

Accounting

Refer to Target Corporation's financial statements (http://www.targetcorp.com/targetcorp_group/investor-relations/investor-relations.jhtml) . Target Corporation is currently seeking additional capital to expand its operations. Two companies have shown interest in providing additional capital. Company #1 is interested in investing in the organization and, therefore, would like to have part ownership through the sale of new stock. Company #2 is interested in providing a loan to the Target Corporation. Both organizations need to know more about the financial stability of Target. As an employee of Target, your supervisor needs you to write a memo in which you explain what infor... click for more

Stochastic Differential Equations (density functions/random variables)

(See attached file for full problem description)

Find QR decomposition to solve the least squares solution

I'm stuck with a question about calculating QR decomposition and to solve the at least square solution. I'm wondering if anyone who can help me here. Thanks in advance. Question is attached.